Chapter 3: Q. 3.45 (page 272)

Use slopes to determine if the lines are perpendicular:
ⓐ $y = - 3 x + 2$ and $x - 3 y = 4$
ⓑ $5 x + 4 y = 1$ and $4 x + 5 y = 3$

Short Answer

Expert verified

ⓐ The given lines are perpendicular.

ⓑ The given lines are not perpendicular.

Step by step solution

Step 1. Given Information

Pair of lines:

ⓐ $y = - 3 x + 2$ and $x - 3 y = 4$

ⓑ $5 x + 4 y = 1$ and $4 x + 5 y = 3$

Step 2. Required to find

Use slopes to determine if the lines are perpendicular.

Step 3. Convert the equations into slope and y-intercept form

If the co-efficient of y is not 1, divide the equations by the co-efficient of y, rearrange the terms to make equation of the form $y = m x + b$ .

the equations become:

ⓐ $y = - 3 x + 2$ and $y = \frac{1}{3} x - \frac{4}{3}$

ⓑ $y = - \frac{5}{4} x + \frac{1}{4}$ and role="math" localid="1645505131317" $y = - \frac{4}{5} x + \frac{3}{5}$

Step 4. Use the slopes to check perpendicularity

The slopes are negative reciprocals of each other, to be perpendicular. We multiply the slopes and check for product to be equal to $- 1$ :

ⓐ $m_{1} \times m_{2} = - 3 \times \frac{1}{3} = - 1$ . Therefore, the given lines are perpendicular.

ⓑ $m_{1} \times m_{2} = - \frac{5}{4} \times - \frac{4}{5} = 1$ . Therefore, the given lines are not perpendicular.

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Use slopes to determine if the lines are perpendicular:
ⓐ $y = - 3 x + 2$ and $x - 3 y = 4$
ⓑ $5 x + 4 y = 1$ and $4 x + 5 y = 3$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Required to find

Step 3. Convert the equations into slope and y-intercept form

Step 4. Use the slopes to check perpendicularity

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Use slopes to determine if the lines are perpendicular:ⓐ y=-3x+2and x-3y=4ⓑ 5x+4y=1and 4x+5y=3

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Required to find

Step 3. Convert the equations into slope and y-intercept form

Step 4. Use the slopes to check perpendicularity

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

Mechanics Maths

Geometry

Calculus

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Use slopes to determine if the lines are perpendicular:
ⓐ $y = - 3 x + 2$ and $x - 3 y = 4$
ⓑ $5 x + 4 y = 1$ and $4 x + 5 y = 3$